"Cette femme est plus âgée que je ne suis."
I've only ever seen "ne" used for negation. It doesn't seem to be negating anything here, though. Can anyone tell me the function of "ne" in this sentence?
It's called a "ne" explétif, which means that this adverb is not mandatory and has nothing to do with the negation one ("ne...pas").
It only appears in subordinates parts (after "que") with certain verbs or constructions like the present example.
By the way, the usual form of this sentence is more often : Cette femme est plus âgée que moi.
By the way, the correct form is "cette femme est plus âgée que je ne LE suis".
Its function is the replacement of "âgée". Yet I must admit that this turn of phrase has more words than necessary. To say the same thing, enough to say "elle est plus âgée que moi".
I was told "This woman is more elderly than I" is wrong. I don't think it's the best sentence in the world but I don't think it's technically wrong, thoughts?
Yes it is, because "elderly" is a noun, a polite word for "old person". Therefore you cannot use a comparative (more... or less...) with a noun, only with an adjective.
the simple adjective "old" is sufficient.
In French : "vieux" (singular/plural - masculine) and "vieille" or "vieilles" (singular or plural - feminine)
Elderly is an adjective not a noun. "An elder" is a noun. http://dictionary.reference.com/browse/elderly?s=t
Because it's an adjective with 3 syllables it therefore requires the use of most/more/less etc before it when used as a comparative or superlative.
It certainly isn't a very common statement though, so probably not worth including here.
Elderly can be used as both, for instance the elderly come here often. But I would consider you correct also.